Show that for any x0 in R there exists a unique global solution x: R->R of the initial value problem
x’(t) = (x(t)2 + t)sin(x(t))
x(0) = x0
could anyone please help me to do this question ?? ,, ,
Picard?Lindelöf theorem - Wikipedia, the free encyclopedia
The big part is to prove that f(t,x)=(x^2+t)sin(x) is Lipschitz continuous in y, uniformly continuous in t. For that, the mean value theorem would be helpful.